Is there a way to delete bone constraints by name?
Delete the constraints with name &quot;Action&quot; or delete the constraints from bone which contain &quot;Action&quot; in bone's name? I will assume the later one in my following answer:


Use bone.constraints.remove(constraint) instead of operator. armature - delete bone constraint in python

Directly use what you get from for loop


import bpy

for bone in bpy.context.selected_pose_bones:
    if 'Action' in bone.name:
        # Iterate over all the bone's constraints and delete them all
        for c in bone.constraints:
            bone.constraints.remove(c)  # Remove constraint


import bpy

for bone in bpy.context.selected_pose_bones:
    for c in bone.constraints:
        if 'Action' in c.name:
            bone.constraints.remove(c)  # Remove constraint